Euclidean Metric
Definition
The Euclidean metric is the standard metric on \(\mathbb{R}^{n}\), defined as:
\[ d(x, y) = \sqrt{\sum_{i = 1}^{n} (x_{i} - y_{i})^{2}}.\]
In \(\mathbb{R}\) this is equivalent to the absolute value function, and in \(\mathbb{R}\), \(\mathbb{R}^{2}\) and \(\mathbb{R}^{3}\) it is equivalent to the intuitive notion of measuring distances, equivalent to the Pythagorean theorem.